Problem: Simplify the following expression: $z = \dfrac{-2t^2 + 30t - 112}{t - 8} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ z =\dfrac{-2(t^2 - 15t + 56)}{t - 8} $ Then we factor the remaining polynomial: $t^2 {-15}t + {56} $ ${-8} {-7} = {-15}$ ${-8} \times {-7} = {56}$ $ (t {-8}) (t {-7}) $ This gives us a factored expression: $\dfrac{-2(t {-8}) (t {-7})}{t - 8}$ We can divide the numerator and denominator by $(t + 8)$ on condition that $t \neq 8$ Therefore $z = -2(t - 7); t \neq 8$